Problem: Express this quotient in scientific notation: ${\frac{3.510\times 10^{8}} {9.0\times 10^{1}}}$
Start by collecting like terms together. $= {\frac{3.510} {9.0}} \times{\frac{10^{8}} {10^{1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.39 \times 10^{8\,-\,1}$ $= 0.39 \times 10^{7}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.39$ is the same as $3.90 \div 10$ , or $3.90 \times 10^{-1}$ $ = {3.90 \times 10^{-1}} \times 10^{7} $ $= 3.90\times 10^{6}$